Finite Group Databasebeta

← #11780253

Subgroups — #11780253

Order 1152.

435 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 435 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593863C211yesmaximal, characteristic
2C3×#4682C211yesmaximal, characteristic, complemented
3#10590363C211yesmaximal, characteristic
4#10590307C211yesmaximal, characteristic, complemented
5#10589322C211yesmaximal, characteristic, complemented
6C3×#4459C211yesmaximal, characteristic
7#10589092C211yesmaximal, characteristic, complemented
8#71370—31nomaximal
9#68209—31nomaximal
10C4×#634C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63863—21no—
15#63858—22no—
16#63857—21no—
17#63843—21no—
18#63841—21no—
19C2×#3715—21no—
20C32×C4×C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#818—22no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63573—21no—
25#63567—21no—
26#63565—21no—
27#5732—31no—
28#5542—31no—
29C3×#500—31no—
30#5094—31no—
31#5083—31no—
32#5019—31no—
33#4851—31no—
34#4682D311yescharacteristic, complemented
35C3×D4⋊C8—31no—
36#4547—31no—
37#4486—31no—
38#4459D311yescharacteristic
39#4456—31no—
40#4456—31no—
41#4456—61no—
42C2×#634D411yescharacteristic
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6—21no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)D411yescharacteristic
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×C4⋊Dic3D412yes—
59C2×C3×C3⋊C8—21no—
60Dic3⋊Dic3—22no—
61(C2×D3)⋊Dic3—22no—
62(C2×D3)⋊Dic3—22no—
63Dic32—22no—
64#3715—42no—
65#1650—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—31no—
68C3×C4×D4—31no—
69#947—61no—
70Q8×Dic3—61no—
71C2×#215—61no—
72#936—61no—
73C2×#214—61no—
74#926—61no—
75#924—61no—
76#898—62no—
77#897—61no—
78#892—61no—
79#887—61no—
80#879—62no—
81C4×D12C2×D311yescharacteristic
82#869C2×D311yescharacteristic
83#869C2×D311yescharacteristic
84C4×Dic6—31no—
85C4×Dic6—31no—
86C4×Dic6—61no—
87C3×#107—62no—
88C3×C4⋊C8—31no—
89C3×C4×C8—21no—
90C3×C4×C8C2×D311yescharacteristic
91C3×C4×C8C2×D311yescharacteristic
92#835—61no—
93#818—22no—
94#817—61no—
95#816—61no—
96#810—61no—
97#810—61no—
98#808—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—21no—
109#634—21no—
110#634—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—41no—
114C3×D12—21no—
115C3×D12—21no—
116C3×C4×D3—41no—
117C3×C4×D3—41no—
118C3×Dic6—41no—
119C3×Dic6—41no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C32×C8—22no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—41no—
125#556—91no—
126#500—31no—
127#475—91no—
128#461—91no—
129#332—91no—
130Q8⋊C8—91no—
131D4⋊C8—31no—
132C2×C3×Q8—61no—
133C2×C3×Q8—61no—
134C2×C3×D4—31no—
135C22×C3×C4—61no—
136C2×D12D1211yescharacteristic
137C2×C4×D3—21no—
138C2×Dic6—21no—
139C2×Dic6—21no—
140C2×Dic6—31no—
141C2×Dic6—31no—
142C2×Dic6—61no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—41no—
146C2×C3×C8—61no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—32no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C22⋊C4—61no—
153C3×C42—21no—
154C3×C42C22×D311yescharacteristic
155C3×C42C22×D311yescharacteristic
156#217—62no—
157#217—62no—
158#215—122no—
159#214—122no—
160(C2×D3)⋊C4—21no—
161(C2×D3)⋊C4—62no—
162(C2×D3)⋊C4—62no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C4⋊Dic3—21no—
166C4⋊Dic3—31no—
167C4⋊Dic3—31no—
168C4⋊Dic3—61no—
169C4⋊Dic3—62no—
170C4⋊Dic3D1211yescharacteristic
171C4⋊Dic3#6712yes—
172Dic3⋊C4—62no—
173Dic3⋊C4—61no—
174Dic3⋊C4—61no—
175Dic3⋊C4—121no—
176C4×Dic3—62no—
177C4×Dic3—62no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180C4×Dic3—121no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—121no—
185C22×C32#12011yescharacteristic
186C2×C3×D3—41no—
187C2×C3×D3—41no—
188C2×C3×D3—41no—
189C32×C4—21no—
190C32×C4#13511yescharacteristic
191C32×C4#13511yescharacteristic
192C32×C4AGL(1,ℤ/8)11yescharacteristic
193C32×C4#13711yescharacteristic
194C3⋊Dic3—41no—
195C3⋊Dic3—41no—
196C3×Dic3—42no—
197C3×Dic3—41no—
198C3×Dic3—81no—
199C2×SD16—181no—
200C4⋊Q8—31no—
201C4⋊Q8—31no—
202#126—182no—
203#124—181no—
204C22⋊Q8—181no—
205C4×Q8—91no—
206C4×Q8—181no—
207C4×D4—31no—
208#117—181no—
209#107—62no—
210#106—181no—
211C4⋊C8—31no—
212C4⋊C8—91no—
213#103—181no—
214#103—181no—
215C4×C8D3211yescharacteristic
216C23×C3—61no—
217C22×D3—21no—
218C3×Q8—121no—
219C3×Q8—121no—
220C3×Q8—121no—
221C3×Q8—121no—
222C3×D4—61no—
223C3×D4—61no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—62no—
228C2×C3×C4—61no—
229C2×C3×C4—121no—
230C2×C3×C4—121no—
231C2×C3×C4—121no—
232C2×C3×C4C2×D1211yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—22no—
240C2×Dic3—41no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—121no—
246C2×Dic3—121no—
247D12—21no—
248D12—21no—
249C4×D3—41no—
250C4×D3—41no—
251Dic6—41no—
252Dic6—41no—
253Dic6—41no—
254Dic6—41no—
255Dic6—62no—
256Dic6—61no—
257Dic6—61no—
258Dic6—61no—
259Dic6—61no—
260Dic6—121no—
261C3×C8—22no—
262C3×C8—22no—
263C3×C8—42no—
264C3×C8—121no—
265C3⋊C8—41no—
266C3⋊C8—121no—
267C3⋊C8—121no—
268C3⋊C8—241no—
269C2×C32#44911yescharacteristic
270C2×C32#45211yescharacteristic
271C2×C32#45611yescharacteristic
272C3×D3—81no—
273C2×Q8—61no—
274C2×Q8—61no—
275C2×Q8—91no—
276C2×D4—31no—
277C22×C4—61no—
278SD16—362no—
279C2×C8—21no—
280C2×C8—61no—
281C2×C8—181no—
282C4⋊C4—31no—
283C4⋊C4—32no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4—91no—
288C4⋊C4—182no—
289C4⋊C4—181no—
290C22⋊C4—61no—
291C22⋊C4—182no—
292C22⋊C4—182no—
293C42—182no—
294C42—181no—
295C42C2×D3211yescharacteristic
296C22×C3—21no—
297C22×C3—121no—
298C22×C3—121no—
299C22×C3—121no—
300C22×C3#88211yescharacteristic
301C22×C3#93711yescharacteristic
302C2×D3—41no—
303C2×D3—41no—
304C2×D3—41no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—121no—
313C3×C4—122no—
314C3×C4—241no—
315C3×C4#90411yescharacteristic
316C3×C4#90811yescharacteristic
317C3×C4#91111yescharacteristic
318C3×C4#91211yescharacteristic
319C3×C4#91211yescharacteristic
320C3×C4#91511yescharacteristic
321C3×C4#91811yescharacteristic
322C3×C4#91911yescharacteristic
323Dic3—42no—
324Dic3—41no—
325Dic3—81no—
326Dic3—122no—
327Dic3—121no—
328Dic3—121no—
329Dic3—121no—
330Dic3—121no—
331Dic3—241no—
332C32#165011yescharacteristic, complemented, Sylow
333C23—61no—
334Q8—121no—
335Q8—121no—
336Q8—121no—
337Q8—121no—
338Q8—181no—
339Q8—181no—
340D4—61no—
341D4—61no—
342C2×C4—61no—
343C2×C4—62no—
344C2×C4—121no—
345C2×C4—121no—
346C2×C4—121no—
347C2×C4—181no—
348C2×C4—181no—
349C2×C4D3×D1211yescharacteristic
350C2×C4#380211yescharacteristic
351C2×C4D3×#6711yescharacteristic
352C8—22no—
353C8—121no—
354C8—361no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—241no—
359C2×C3#473411yescharacteristic
360C2×C3#478311yescharacteristic
361C2×C3#482611yescharacteristic
362C2×C3#509511yescharacteristic
363C2×C3#515811yescharacteristic
364C2×C3#518711yescharacteristic
365D3—81no—
366C22—121no—
367C22—121no—
368C22—121no—
369C22#6392211yescharacteristic
370C4—21no—
371C4—122no—
372C4—121no—
373C4—241no—
374C4—361no—
375C4—361no—
376C4#6379511yescharacteristic
377C4#6380711yescharacteristic
378C4#6381011yescharacteristic
379C4#6381111yescharacteristic
380C3—21no—
381C3#6820911yescharacteristic, complemented
382C3#7137011yescharacteristic, complemented
383C2—241no—
384C2#1059039911yescharacteristic
385C2#1059096211yescharacteristic
386C2#1059096511yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4×C8D32
hypocenterC32#1650
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×#4682C2semidirect
4. #10590307C2semidirect
5. #10589322C2semidirect
7. #10589092C2semidirect
34. #4682D3semidirect
332. C32#1650semidirect
381. C3#68209semidirect
382. C3#71370semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105938632
C3×#46822
#105903632
#105903072
#105893222
C3×#44592
#105890922
#713703
#682093